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Mathematics > Logic

Title:
On Subcomplete Forcing

Abstract: I survey an array of topics in set theory in the context of a novel class of
forcing notions: subcomplete forcing. Subcompleteness was originally defined by
Ronald Jensen. I have attempted to make the subject somewhat more approachable
to set theorists, while showing various properties of subcomplete forcing which
one might desire of a forcing class, drawing comparisons between subcomplete
forcing and countably closed forcing. In particular, I look at the interaction
between subcomplete forcing and $\omega_1$-trees, preservation properties of
subcomplete forcing, the subcomplete maximality principle, the subcomplete
resurrection axiom, and show that generalized diagonal Prikry forcing is
subcomplete.